Systems of Linear Equations and Polynomial Equations
Solve a linear system Solve a polynomial equation

Solve a linear system

Suppose you have the following system to solve:

\[ \begin{cases} 3x + 4y - 5z = -3.5 \\ x - y + z = 1.5 \\ x - 3y + 6z = 16 \end{cases} \]

All the equations must be in the form \(a \cdot x + b \cdot y + c \cdot z = d\).

  1. Press Menu Icon, select Algebra > Solve System of Equations > Solve System of Linear Equation.
  2. Enter 3 as the number of equations and fill it as follows:

    Linear System Screenshot

  3. We have 3 equations and 3 unknowns (\(x\), \(y\), and \(z\)).

    Press Enter Icon. The results should be \(x = 1\), \(y = 4\), and \(z = 4.5\).

Solve a Polynomial Equation

Suppose you have to solve the equation \(x^3 - 10x^2 + 33x - 36 = 0\).

The right-hand side must be 0.

  1. Press Menu Icon, select Algebra > Polynomial Tools > Find Roots of Polynomial. Set 3 as the order of the equation. Fill the equation as follows:

    Polynomial Step 1 Screenshot

    The order is the biggest power of \(x\) in the equation.

  2. Press Enter Icon. The results should be 3 and 4:

    Polynomial Step 1 Screenshot

    \(3\) appears twice because \(x^3 - 10x^2 + 33x - 36 = (x - 3)(x - 3)(x - 4)\).